2019/12/15 by Herbert Egger, Egger, Herbert, Bogdan Radu +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1912.07057
openalex publication_date 2019/12/15 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28
We consider the efficient numerical approximation of acoustic wave propagation in time domain by a finite element method with mass lumping. In the presence of internal damping, the problem can be reduced to a second order formulation in time for the velocity field alone. For the spatial approximation we consider H(div)--conforming finite elements of second order. In order to allow for an efficient time integration, we propose a mass-lumping strategy based on approximation of the L2-scalar product by inexact numerical integration which leads to a block-diagonal mass matrix. A careful error analysis allows to show that second order accuracy is not reduced by the quadrature errors which is illustrated also by numerical tests.